Subgroups — #26267274

Order 12032.

916 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253845	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689383	C₂	1	2	yes	maximal, complemented
3	#20252852	C₂	1	1	yes	maximal, characteristic
4	#20252131	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244688	C₂	1	2	yes	maximal, complemented
6	#20244500	C₂	1	2	yes	maximal, complemented
7	#20244233	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244164	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243906	C₂	1	2	yes	maximal, complemented
10	C₄×#13093941	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094055	C₂²	1	2	yes	—
13	C₂×#13094055	C₂²	1	2	yes	—
14	C₂×#13094050	C₂²	1	2	yes	—
15	C₂×#13094030	C₂²	1	2	yes	—
16	#15689673	C₂²	1	1	yes	characteristic
17	#15689515	—	2	2	no	—
18	#15689502	—	2	1	no	—
19	#15689497	—	2	1	no	—
20	#15689383	—	2	8	no	—
21	#15689338	—	2	2	no	—
22	#15689328	—	2	1	no	—
23	#15689318	—	2	1	no	—
24	#15689200	—	2	1	no	—
25	#15689193	—	2	2	no	—
26	#15689188	—	2	1	no	—
27	C₂×#13093960	C₂²	1	2	yes	—
28	#15689147	C₂²	1	1	yes	characteristic
29	#15689122	C₂²	1	2	yes	—
30	C₂×#13093943	C₂²	1	2	yes	—
31	C₂×#13093943	C₂²	1	2	yes	—
32	C₂×#13093941	C₂²	1	1	yes	characteristic
33	C₂×#13093941	C₂²	1	1	yes	characteristic
34	#15689089	C₂²	1	2	yes	—
35	C₄×#10625329	C₂²	1	1	yes	characteristic
36	C₄×#10625329	C₂²	1	1	yes	characteristic
37	#15688892	C₂²	1	1	yes	characteristic
38	#15688892	C₂²	1	1	yes	characteristic
39	#15688888	C₂²	1	2	yes	—
40	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#461	—	2	1	no	—
44	C₄₇×#461	—	2	2	no	—
45	C₄₇×#461	—	2	1	no	—
46	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#103×C₄₇	C₂²	1	2	yes	—
48	C₂×#10625350	C₂³	1	2	yes	—
49	#13094055	—	2	4	no	—
50	#13094055	—	2	4	no	—
51	#13094055	—	4	2	no	—
52	#13094055	—	4	2	no	—
53	#13094050	—	2	4	no	—
54	#13094050	—	4	2	no	—
55	C₂×#10625337	—	2	2	no	—
56	C₂×#10625337	—	2	2	no	—
57	C₂×#10625335	—	2	2	no	—
58	C₂×#10625336	—	2	2	no	—
59	C₂×#10625336	—	2	2	no	—
60	C₂×#10625334	—	2	2	no	—
61	#13094030	—	2	4	no	—
62	#13094030	—	4	2	no	—
63	C₂×#10625329	C₂³	1	1	yes	characteristic
64	C₂×#10625329	C₂³	1	2	yes	—
65	C₂×#10625329	C₂³	1	1	yes	characteristic
66	C₂×#10625329	C₂³	1	1	yes	characteristic
67	C₂×#10625329	C₂³	1	1	yes	characteristic
68	C₂×#10625324	—	2	2	no	—
69	C₂×C₈×D₄₇	—	2	2	no	—
70	#13094024	D₄	1	1	yes	characteristic
71	#13094021	D₄	1	1	yes	characteristic
72	#13094012	D₄	1	2	yes	—
73	#13093998	—	2	1	no	—
74	#13093998	—	2	1	no	—
75	C₄×D₁₈₈	—	2	1	no	—
76	C₄×D₁₈₈	—	2	1	no	—
77	#13093960	—	2	4	no	—
78	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
79	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
80	#13093947	—	2	2	no	—
81	#13093944	—	2	2	no	—
82	#13093943	—	2	4	no	—
83	#13093943	—	4	2	no	—
84	#13093941	—	2	2	no	—
85	#13093941	D₄	1	4	yes	complemented
86	(C₂×D₄₇)⋊C₈	—	2	2	no	—
87	(C₂×D₄₇)⋊C₈	—	2	2	no	—
88	#13093935	—	2	1	no	—
89	#13093935	—	2	1	no	—
90	C₄×C₄₇⋊C₈	—	2	1	no	—
91	C₄×C₄₇⋊C₈	—	2	1	no	—
92	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₄₇	—	2	1	no	—
95	C₂×SD₁₆×C₄₇	—	2	4	no	—
96	C₂×SD₁₆×C₄₇	—	2	2	no	—
97	C₂×SD₁₆×C₄₇	—	2	2	no	—
98	C₂×SD₁₆×C₄₇	—	4	2	no	—
99	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
100	C₄⋊Q₈×C₄₇	—	2	1	no	—
101	C₄⋊Q₈×C₄₇	—	2	1	no	—
102	C₄⋊Q₈×C₄₇	—	2	1	no	—
103	C₄⋊Q₈×C₄₇	—	2	1	no	—
104	C₄×D₄×C₄₇	—	2	1	no	—
105	C₄×D₄×C₄₇	—	2	1	no	—
106	C₄×D₄×C₄₇	—	2	1	no	—
107	C₄×D₄×C₄₇	—	2	1	no	—
108	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
112	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
114	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
115	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
116	#103×C₄₇	—	2	2	no	—
117	#103×C₄₇	—	2	2	no	—
118	C₂⁴×C₄₇	—	2	1	no	—
119	C₂×Q₈×C₄₇	—	2	2	no	—
120	C₂×Q₈×C₄₇	—	2	2	no	—
121	C₂×Q₈×C₄₇	—	2	2	no	—
122	C₂×Q₈×C₄₇	—	2	2	no	—
123	C₂×Q₈×C₄₇	—	2	2	no	—
124	C₂×Q₈×C₄₇	—	2	2	no	—
125	C₂×D₄×C₄₇	—	2	1	no	—
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	—	2	1	no	—
129	C₂×D₄×C₄₇	—	2	1	no	—
130	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	4	1	no	—
134	C₂²×C₄×C₄₇	—	4	1	no	—
135	C₂²×C₄×C₄₇	—	8	2	no	—
136	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
139	C₂×C₂²⋊D₄₇	—	2	2	no	—
140	#10625350	—	2	2	no	—
141	#10625350	—	2	2	no	—
142	#10625350	—	2	2	no	—
143	#10625350	—	2	2	no	—
144	C₂×D₁₈₈	—	2	1	no	—
145	C₂×D₁₈₈	—	2	1	no	—
146	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
147	C₂×C₄×D₄₇	—	2	2	no	—
148	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
149	SD₁₆×C₄₇	—	4	4	no	—
150	SD₁₆×C₄₇	—	4	4	no	—
151	C₂×C₈×C₄₇	—	2	2	no	—
152	C₂×C₈×C₄₇	—	2	2	no	—
153	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₄₇	—	2	1	no	—
156	C₄⋊C₄×C₄₇	—	2	1	no	—
157	C₄⋊C₄×C₄₇	—	4	1	no	—
158	C₄⋊C₄×C₄₇	—	4	1	no	—
159	C₄⋊C₄×C₄₇	—	4	1	no	—
160	C₄⋊C₄×C₄₇	—	4	1	no	—
161	C₂²⋊C₄×C₄₇	—	4	1	no	—
162	C₂²⋊C₄×C₄₇	—	4	1	no	—
163	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
167	#10625337	—	4	4	no	—
168	#10625337	—	4	4	no	—
169	#10625336	—	4	4	no	—
170	#10625336	—	4	4	no	—
171	#10625335	—	4	4	no	—
172	#10625334	—	4	4	no	—
173	(C₂×D₄₇)⋊C₄	—	2	2	no	—
174	(C₂×D₄₇)⋊C₄	—	2	2	no	—
175	C₄⋊Dic₄₇	—	2	1	no	—
176	C₄⋊Dic₄₇	—	2	1	no	—
177	#10625329	—	2	1	no	—
178	#10625329	—	2	1	no	—
179	#10625329	—	2	1	no	—
180	#10625329	—	2	2	no	—
181	#10625329	—	2	1	no	—
182	#10625329	—	2	1	no	—
183	#10625329	—	2	2	no	—
184	#10625329	C₂×D₄	1	2	yes	—
185	#10625329	C₂×D₄	1	2	yes	—
186	#10625329	#41	1	2	yes	—
187	C₂×C₄₇⋊C₈	—	2	1	no	—
188	C₂×C₄₇⋊C₈	—	2	1	no	—
189	C₂×C₄₇⋊C₈	—	2	1	no	—
190	C₂×C₄₇⋊C₈	—	2	1	no	—
191	C₂×C₄₇⋊C₈	—	2	2	no	—
192	#10625324	—	4	4	no	—
193	C₈×D₄₇	—	4	4	no	—
194	C₂³×C₄₇	—	2	2	no	—
195	C₂³×C₄₇	—	4	1	no	—
196	C₂³×C₄₇	—	4	1	no	—
197	C₂³×C₄₇	—	8	1	no	—
198	C₂³×C₄₇	—	8	1	no	—
199	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂²×D₄₇	—	2	2	no	—
201	Q₈×C₄₇	—	4	2	no	—
202	Q₈×C₄₇	—	4	2	no	—
203	Q₈×C₄₇	—	4	2	no	—
204	Q₈×C₄₇	—	4	2	no	—
205	D₄×C₄₇	—	2	2	no	—
206	D₄×C₄₇	—	2	2	no	—
207	D₄×C₄₇	—	4	1	no	—
208	D₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	8	2	no	—
216	C₂×C₄×C₄₇	—	8	2	no	—
217	C₂×C₄×C₄₇	—	8	1	no	—
218	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
219	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂²⋊D₄₇	—	4	2	no	—
229	C₂²⋊D₄₇	—	4	2	no	—
230	C₂×Dic₄₇	—	2	2	no	—
231	D₁₈₈	—	2	2	no	—
232	D₁₈₈	—	2	2	no	—
233	D₁₈₈	—	4	2	no	—
234	D₁₈₈	—	8	1	no	—
235	C₄×D₄₇	—	4	2	no	—
236	C₄×D₄₇	—	4	2	no	—
237	Dic₉₄	—	2	2	no	—
238	Dic₉₄	—	2	2	no	—
239	C₈×C₄₇	—	2	2	no	—
240	C₈×C₄₇	—	2	2	no	—
241	C₄₇⋊C₈	—	2	2	no	—
242	C₄₇⋊C₈	—	2	2	no	—
243	C₄₇⋊C₈	—	2	2	no	—
244	C₄₇⋊C₈	—	4	2	no	—
245	C₄₇⋊C₈	—	4	1	no	—
246	#25405	—	47	1	no	maximal, Sylow
247	C₂²×C₄₇	—	2	1	no	—
248	C₂²×C₄₇	—	2	1	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	8	2	no	—
251	C₂²×C₄₇	—	8	2	no	—
252	C₂²×C₄₇	—	8	1	no	—
253	C₂²×C₄₇	—	8	1	no	—
254	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
255	C₂²×C₄₇	#532	1	1	yes	characteristic
256	C₂²×C₄₇	#540	1	1	yes	characteristic
257	C₂×D₄₇	—	4	2	no	—
258	C₂×D₄₇	—	4	2	no	—
259	C₂×D₄₇	—	4	2	no	—
260	C₄×C₄₇	—	2	1	no	—
261	C₄×C₄₇	—	2	1	no	—
262	C₄×C₄₇	—	2	1	no	—
263	C₄×C₄₇	—	8	2	no	—
264	C₄×C₄₇	—	8	1	no	—
265	C₄×C₄₇	#471	1	2	yes	complemented
266	C₄×C₄₇	D₄²	1	1	yes	characteristic
267	C₄×C₄₇	D₄²	1	1	yes	characteristic
268	C₄×C₄₇	#546	1	1	yes	characteristic
269	C₄×C₄₇	#550	1	1	yes	characteristic
270	Dic₄₇	—	4	2	no	—
271	#3152	—	47	1	no	—
272	C₂×#471	—	47	2	no	—
273	#3036	—	47	1	no	—
274	C₂×#461	D₄₇	1	1	yes	characteristic, complemented
275	#2935	—	47	1	no	—
276	#2052	—	47	2	no	—
277	#2019	—	47	2	no	—
278	#1966	—	47	1	no	—
279	#1950	—	47	1	no	—
280	#1908	—	47	2	no	—
281	C₄×#100	—	47	1	no	—
282	C₂×C₄₇	—	2	1	no	—
283	C₂×C₄₇	—	2	1	no	—
284	C₂×C₄₇	—	8	2	no	—
285	C₂×C₄₇	#2428	1	1	yes	characteristic
286	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
287	C₂×C₄₇	#3069	1	1	yes	characteristic
288	D₄₇	—	8	2	no	—
289	C₂×#137	—	47	2	no	—
290	C₂×#137	—	47	2	no	—
291	C₂×AGL(1,ℤ/8)	—	47	2	no	—
292	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
293	C₂×#131	—	47	2	no	—
294	#532	—	47	1	no	—
295	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
296	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
297	#497	—	94	2	no	—
298	#494	—	94	1	no	—
299	#492	—	94	1	no	—
300	#471	—	94	8	no	—
301	#463	—	94	2	no	—
302	#461	—	2	1	no	—
303	#461	—	2	2	no	—
304	#461	—	2	1	no	—
305	#461	—	94	1	no	—
306	#459	—	94	1	no	—
307	#436	—	94	1	no	—
308	#435	—	94	2	no	—
309	C₈×D₄	—	94	1	no	—
310	C₂×#108	—	47	2	no	—
311	#423	—	47	1	no	—
312	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
313	#417	—	47	2	no	—
314	C₂×#103	C₂×D₄₇	1	2	yes	—
315	C₂×#101	—	47	2	no	—
316	C₂×#101	—	47	2	no	—
317	C₂×#100	—	47	1	no	—
318	C₂×#100	—	47	1	no	—
319	#408	—	47	2	no	—
320	C₄×M₁₆	—	47	1	no	—
321	C₄×M₁₆	—	47	1	no	—
322	#343	—	47	1	no	—
323	#343	—	47	1	no	—
324	#341	—	47	2	no	—
325	C₄₇	#25405	1	1	yes	characteristic, complemented, Sylow
326	C₂×#41	—	47	2	no	—
327	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
328	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
329	C₂³×C₄	—	2	1	no	—
330	#137	—	94	4	no	—
331	#137	—	94	4	no	—
332	#137	—	188	2	no	—
333	#137	—	188	2	no	—
334	AGL(1,ℤ/8)	—	94	4	no	—
335	AGL(1,ℤ/8)	—	188	2	no	—
336	C₂×Q₁₆	—	94	2	no	—
337	C₂×Q₁₆	—	94	2	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	4	2	no	—
342	C₂×SD₁₆	—	94	2	no	—
343	C₂×SD₁₆	—	94	2	no	—
344	C₂×SD₁₆	—	94	2	no	—
345	C₂×D₈	—	94	2	no	—
346	#131	—	94	4	no	—
347	#131	—	188	2	no	—
348	C₂×M₁₆	—	47	1	no	—
349	C₂×M₁₆	—	47	1	no	—
350	C₂×M₁₆	—	47	1	no	—
351	C₂×M₁₆	—	47	2	no	—
352	C₂×M₁₆	—	47	1	no	—
353	C₂×M₁₆	—	94	2	no	—
354	C₂²×C₈	—	94	2	no	—
355	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	—	47	1	no	—
361	#127	—	47	1	no	—
362	#124	—	47	2	no	—
363	#121	—	94	1	no	—
364	#121	—	94	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	94	1	no	—
370	C₄×D₄	—	94	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
376	#108	—	94	4	no	—
377	C₄⋊C₈	—	94	1	no	—
378	C₄⋊C₈	—	94	1	no	—
379	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
380	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
381	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
382	#103	—	2	2	no	—
383	#103	—	2	2	no	—
384	#103	—	94	2	no	—
385	#102	—	94	2	no	—
386	#101	—	94	4	no	—
387	#101	—	188	2	no	—
388	#100	—	47	4	no	—
389	#100	—	94	2	no	—
390	C₂²⋊C₈	—	94	2	no	—
391	C₂²⋊C₈	—	94	2	no	—
392	#97	—	94	1	no	—
393	#97	—	94	1	no	—
394	C₄×C₈	—	94	1	no	—
395	C₄×C₈	—	94	1	no	—
396	C₂⁴	—	2	1	no	—
397	#41	—	94	2	no	—
398	#41	—	94	2	no	—
399	#41	—	94	2	no	—
400	#41	—	94	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	47	2	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	47	2	no	—
414	C₂×D₄	—	94	2	no	—
415	C₂×D₄	—	94	1	no	—
416	C₂×D₄	—	94	1	no	—
417	C₂×D₄	D₄×D₄₇	1	2	yes	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	4	1	no	—
421	C₂²×C₄	—	4	1	no	—
422	C₂²×C₄	—	8	2	no	—
423	C₂²×C₄	—	94	2	no	—
424	C₂²×C₄	#10625352	1	1	yes	characteristic
425	C₂²×C₄	#10625352	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
427	Q₁₆	—	188	4	no	—
428	Q₁₆	—	188	4	no	—
429	SD₁₆	—	4	4	no	—
430	SD₁₆	—	4	4	no	—
431	SD₁₆	—	188	4	no	—
432	SD₁₆	—	188	4	no	—
433	SD₁₆	—	188	4	no	—
434	D₈	—	188	4	no	—
435	M₁₆	—	47	2	no	—
436	M₁₆	—	47	2	no	—
437	M₁₆	—	47	2	no	—
438	M₁₆	—	94	1	no	—
439	M₁₆	—	94	1	no	—
440	M₁₆	—	94	1	no	—
441	M₁₆	—	94	2	no	—
442	M₁₆	—	94	1	no	—
443	M₁₆	—	94	1	no	—
444	M₁₆	—	94	2	no	—
445	M₁₆	—	188	4	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	94	1	no	—
449	C₂×C₈	—	94	1	no	—
450	C₂×C₈	—	94	1	no	—
451	C₂×C₈	—	94	2	no	—
452	C₂×C₈	—	94	1	no	—
453	C₂×C₈	—	188	4	no	—
454	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
455	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	94	1	no	—
463	C₄⋊C₄	—	94	1	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₂²⋊C₄	—	94	2	no	—
467	C₂²⋊C₄	—	94	2	no	—
468	C₄²	D₄×D₄₇	1	1	yes	characteristic
469	C₄²	D₄×D₄₇	1	1	yes	characteristic
470	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
471	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
472	C₂³	—	2	2	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	8	1	no	—
476	C₂³	—	8	1	no	—
477	C₂³	—	94	2	no	—
478	C₂³	C₂×#10625352	1	1	yes	characteristic
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	94	2	no	—
484	Q₈	—	94	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	2	no	—
487	D₄	—	4	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	94	2	no	—
490	D₄	—	94	2	no	—
491	D₄	—	376	1	no	—
492	D₄	—	188	2	no	—
493	D₄	—	188	2	no	—
494	D₄	—	188	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	1	no	—
504	C₂×C₄	—	94	2	no	—
505	C₂×C₄	—	188	2	no	—
506	C₂×C₄	—	188	2	no	—
507	C₂×C₄	#13093995	1	1	yes	characteristic
508	C₂×C₄	#13093995	1	1	yes	characteristic
509	C₂×C₄	#13093995	1	1	yes	characteristic
510	C₂×C₄	#13093995	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
512	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
513	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
514	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
515	C₂×C₄	#13094069	1	1	yes	characteristic
516	C₂×C₄	#13094070	1	1	yes	characteristic
517	C₈	—	2	2	no	—
518	C₈	—	2	2	no	—
519	C₈	—	94	2	no	—
520	C₈	—	94	2	no	—
521	C₈	—	94	2	no	—
522	C₈	—	188	2	no	—
523	C₈	—	188	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	188	2	no	—
532	C₂²	—	188	2	no	—
533	C₂²	—	188	2	no	—
534	C₂²	C₂×#13093995	1	1	yes	characteristic
535	C₂²	#15689668	1	1	yes	characteristic
536	C₂²	#15689726	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	2	no	—
542	C₄	—	188	2	no	—
543	C₄	#15689383	1	2	yes	complemented
544	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
545	C₄	#15689757	1	1	yes	characteristic
546	C₄	#15689770	1	1	yes	characteristic
547	C₄	#15689792	1	1	yes	characteristic
548	C₂	—	2	1	no	—
549	C₂	—	2	1	no	—
550	C₂	—	8	2	no	—
551	C₂	—	376	2	no	—
552	C₂	#20246972	1	1	yes	characteristic
553	C₂	C₂×#15689383	1	1	yes	characteristic
554	C₂	#20253121	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093995
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#461	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#20252852	C₂
hypercenter	C₂×#461	D₄₇
hypocenter	C₄₇	#25405
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#461

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20253845	C₂	semidirect
2. C₂×#15689383	C₂	semidirect
4. #20252131	C₂	semidirect
5. #20244688	C₂	semidirect
6. #20244500	C₂	semidirect
7. #20244233	C₂	semidirect
8. #20244164	C₂	semidirect
9. #20243906	C₂	semidirect
10. C₄×#13093941	C₂	semidirect
11. C₂×C₄₇×#461	C₂	semidirect
85. #13093941	D₄	semidirect
265. C₄×C₄₇	#471	semidirect
274. C₂×#461	D₄₇	semidirect
325. C₄₇	#25405	semidirect
543. C₄	#15689383	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20253845	2
C₂×#15689383	2
#20252852	2
#20252131	2
#20244688	2
#20244500	2
#20244233	2
#20244164	2
#20243906	2
C₄×#13093941	2
C₂×C₄₇×#461	2
#25405	47